Trellis coded modulation is a technique for combining coding and modulation to increase channel capacity and improve bit error performance. This coded modulation scheme is based on the concept of mapping by set partitioning described by Ungerboeck in the seminal paper Channel Coding With MultilevellPhase Signals, IEEE Transactions on Information Theory, VoL IT-28, No. 1, January 1982. Trellis coded modulation (TCM) combines coding and modulation operations, thus allowing for improved reliability of the communications system without increasing power or bandwidth requirements. More specifically, the TCM technique combines a higher-order modulation scheme with a convolution type encoding scheme at the transmission end of the system, while the receiving end of the system, instead of performing demodulation and decoding in two separate steps, combines the two operations into one.
A typical TCM scheme involves the mapping of an encoder output directly to a point on a signal constellation, such as an 8-PSK constellation. The combination of the encoding and mapping elements is jointly optimized so as to obtain good error performance. For example, an encoder could take two bits as input and have a three-bit output which is mapped to an 8-PSK constellation. In such a case, the encoder would be said to encode at a 2/3 rate, that is, two inputs bits produce three encoded output bits. Since each point in the signal constellation may have one of two possible values in a binary system, it is necessary to have the number of encoded output bits equal to the logarithm base 2 of the number of points in the desired signal constellation. Thus, when an eight point constellation is used, there should be three encoded output bits (i.e. 2.sup.3 =8 points). When the trellis code is received and decoded by the system receiver, each branch of the trellis corresponds to one 8-PSK symbol, which facilitates soft decision decoding.
Implementing rates such as 3/4 using an 8-PSK constellation presents a problem, however. It is desired that the encoded output be mapped to a single signal in the signal constellation. There is no obvious way to map the 4-bit encoded output of a rate 3/4 encoder to an 8-PSK symbol so that there is only one 8-PSK symbol per trellis branch. Using the logarithm base 2 rule discussed above, a 3/4 rate encoder would require at least a 16 point signal constellation. As higher-order signal constellations ultimately require more bandwidth and power resources, there is a need for a practical method of efficiently using smaller signal constellations to modulate encoded output bit streams produced in TCM applications.